Questions tagged [kerr-metric]

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Singularities of the Coordinate Systems

We know that, the singularity of the Schwarzschild metric at $r=2M$ can be removable via coordinate transformation to Kruskal-Szekers . Can we apply a similar argument to the Kerr metric? If so, what'...
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Orbital Photon Speed at the equatorial plane of a rotating black hole

I've been trying to calculate $d\phi/dt$ of photons orbiting a Kerr black hole (Kerr metric in Boyer-Lindquist coordinates) on the equatorial plane, both counter and along with its rotation. So I used ...
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Event horizon of a rotating black hole

For a non-rotating black hole, Schwarzschild radius itself forms the event horizon, but how do we find the event horizon of a rotating Kerr black hole?
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What is the relative importance of the Coriolis term to the precession term in frame dragging by rotating Kerr black holes?

The Wikipedia entry for Thirring precession describes the Coriolis term as separate from the precession term. Is it fair to say that when looking at the dynamics of a rotating black hole, the ...
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Light scattering on the rotating black hole in the Kerr geometry

To simulate light scattering on the rotating black hole we have used this paper and this code. First, we made animation for light beam scattering in the equatorial plane For not equatorial plane the ...
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Where is the black hole horizon in ingoing Kerr coordinates?

In ingoing Kerr coordinates, the metric of the Kerr black hole spacetime is: \begin{equation} ds^2 = -\left(1-\frac{2Mr}{\Sigma}\right)dv^2 +\frac{2Mr}{\Sigma}\left(dr-a \mathrm{sin}^2\theta d\phi\...
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Undefined symbol in Catalogue of Spacetimes (Kerr metric)

In the Catalogue of Spacetimes, in the Kerr metric section, under "General local tetrad", there is a cluster of four equations (strangely labeled 2.14.6a and 2.14.6b!), two of which contain ...
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Exceeding the Kerr black hole spin limit

It is well known that the limit on the angular momentum for a Kerr black hole is given by \begin{equation} 0 \leq a^* \leq 1 \quad \text{where} \quad a^* \equiv \frac{cJ}{GM^2} \end{equation} and $J$ ...
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Kerr metric in Eddington–Finkelstein form

I am searching for a reference in which I can find out the Kerr metric in Eddington–Finkelstein form. I have computed it by hand and I have obtained the following form but I am not sure above all of ...
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GWs from Kerr BHs

A rotating neutron star can emit GW radiation if it has some ellipticity (Maggiore Gravitational Waves Vol I for example), even if we neglect spindown. I would think that a Kerr BH is not a spherical ...
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Quasilocal formalism and computations in Kerr BH

I read an article about quasilocal formalism and calculations in a Kerr BH (this: https://arxiv.org/abs/hep-th/0102001). I was trying to reproduce the results obtained on it, but I found an expression ...
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How does the angular velocity change with latitude in the Kerr metric?

I was told that in the Kerr metric for a black hole, the angular velocity of the horizon depends on the latitude. How exactly? Is it zero at the poles and largest at the horizon? Or is the dependence ...
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Is possible to use black holes to propel a bullet or make a gun? [closed]

I was reading a book from my grandpa about Black Holes, and in one page it says that some objects can obtain some of the kinetic force from the black holes (in specific cases) and can propel ...
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Defining the electric field with a potential in axisymmetric, stationary fluids on Kerr black hole spacetime

So studying the RMHD (relativistic magnetohydrodynamics) equations of a fluid (/plasma) and specifically Maxwell's equation reads as $$ \nabla \times E = - \dfrac{1}{c} \dfrac{\partial B}{\partial t} ...
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Normal vector field of costant time Kerr slice

The the Kerr metric of the Kerr spacetime in Boyer-Lindquist coordinates is given by $$ds^2=-\left(1-\frac{2mr}{\Sigma}\right)dt^2+\frac{\Sigma}{\Delta}dr^2+\Sigma d\theta^2+\left(r^2+a^2+\frac{2mra^2}...
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Can the effective singularity radius of a rotating black hole be measured?

Can the angular velocity of a black hole be measured? I found this article explaining how to measure the spin of a black hole can be measured, though I'm unclear whether 'spin' means angular velocity ...
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Second fundamental form of Kerr timeslice in BL-coordinates

I want to compute the coefficients of the second fundamental form $K$ of a timeslice $\lbrace t=0\rbrace$ in the Kerr metric in Boyer-Lindquist coordinates. I tried to do this via the definition of ...
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Massless Kerr black hole

Kerr metric has the following form: $$ ds^2 = -\left(1 - \frac{2GMr}{r^2+a^2\cos^2(\theta)}\right) dt^2 + \left(\frac{r^2+a^2\cos^2(\theta)}{r^2-2GMr+a^2}\right) dr^2 + \left(r^2+a^2\cos(\...
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A question about transuvection in Kerr spacetime

We know there are Killing vectors in Kerr spacetime. I wonder when doing transuvection on Killing vector, like $\left(\frac{\partial}{\partial t}\right)^\mu \bullet (dt)_\mu$ why it equals to $g_{tt}$ ...
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Is ergosphere without singularity possible?

The ergosphere is created because of the twisting of spacetime by a fast-rotating black hole. Then what if we rotate a non-singular object (I mean just a normal object that is not a black hole) really ...
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Hadamard state in Kerr spacetime

I have heard of the fact (see e.g. here) that there exists no everywhere-regular Hadamard (vacuum) state for quantum field in Kerr spacetime. My understanding is that the Hadamard condition provides &...
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What's the inner ergosphere in a Kerr black hole?

(My book uses the notation "ergosphere" as the hypersurface of static limit, "ergoregion" as the hypervolume within.) Studying the Kerr BH, I've come to the part about horizons and ...
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What do black holes spin relative to?

What do black holes spin relative to?In other words, what is black hole spin measured in relation to? Spinning black holes are different from non-spinning black holes. For instance, they have ...
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Radial outgoing null geodetic in Kerr spacetime

According to Poisson's book A relativist's toolkit, pag 52, with the Schwarzschild metric I can define outgoing radial null geodesic as follows: $$u=t-\int f(r)^{-1} dr$$ where $f(r)=1-\dfrac{2m}{r}$. ...
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Would there be a physical Boundary Condition on Event Horizon for a perturbed Fluid of a Kerr-BH Accretion Disk?

Let's say we have a Steady-State Disk (Fishbone 1976 HD, or an MHD disk). For simplicity, we focus only on $\theta = \pi/2$. If we perturb every physical quantity by the rule $A = A+ \delta A $ (...
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What is the physical shape of a rapidly spinning singularity?

Let's say I have a star 20x the mass of the sun. At the end of its life, it collapses into a black hole. Now correct me if I am wrong, but as it collapses it rotational speed dramatically increases ...
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Question on four-velocity condition for timelike observers

I am a bit rusty on GR, I have the condition $u_{\mu}u^{\mu} = -1 $, in some notes I am given that we can obtain: $$-1 = u^{2}_{t} [g_{tt} +2 \Omega g_{t \phi} + \Omega^{2} g_{\phi\phi}]. \tag{1} $$ ...
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Kerr Metric in Cartesian Coordinates

I have checked online and the Kerr metric never seems to be given in Cartesian coordinates (although there is a conversion factor from Cartesian to Boyer-Lindquist coordinates). Is there some reason ...
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Do spinning object near a spinning black hole obey the equivalence principle?

According to the equivalence principle the path of an object should not depend on it's composition. But on the other hand a spinning object (e.g. an electron) moving past a rotating Kerr black hole ...
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Kerr black hole evaporation time question

Is there any closed (even if complicated) formula por the Hawking evaporation time for a Kerr black hole (and more general black holes) just like the one \begin{equation} t_e=\dfrac{5120\pi G^2M_0^3}{\...
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Time dilatation of an observer falling towards a Kerr Black Hole

In a Kerr Black hole there is a region where the component $g_{t t}$ of the metric changes sign (the ergoregion). The surface where $g_{t t}=0$ is called the ergosphere. So, if we consider an observer ...
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What happens when two ergospheres of oppositely spinning black holes of the same mass, axis of rotation, and speed of rotation approach?

What happens when two ergospheres of oppositely spinning black holes of the same mass, axis of rotation, and speed of rotation approach each other? What would happen to the black holes in question?
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How to show if a world line is null for a particular metric [closed]

For the Kerr metric, with line element $$ ds^2 = -\frac{\Delta-a^2\sin^2\theta}{\rho^2}dt^2 - \frac{4Mar\sin^2\theta}{\rho^2}dtd\phi +\frac{(r^2+a^2)^2-a^2\Delta\sin^2\theta}{\rho^2}\sin^2\theta d\phi^...
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Gravitational Redshift in Kerr Spacetime

Well, suppose then Schwarschild black holes. Following the $[1]$, we have the redshift factor: $$d\tau = \sqrt{1-\frac{2M}{r}}dt. \tag{1}$$ This factor have an physical interpretation to be the ...
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Spin rotation of masses in a rotating gravitational field around a black hole

If a rotational gravitational field affects masses in the way the frame and body velocities are added together does it mean that as the rotation of the frame has a gradient of the perpendicular ...
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Horizons and other special surfaces on Kerr metric

The Kerr metric is \begin{equation} ds^2 = - \big(1-\frac{2GMr}{\rho^2}\big)dt^2-\frac{2GMra}{\rho^2}\sin^2 \theta \big(dtd\phi+d\phi dt\big)+ \frac{\rho^2}{\Delta}dr^2+\rho^2 d\theta^2 + \frac{\sin^...
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Trying to determine physically meaningful initial conditions for test particle around a Kerr black hole

I am working on some code for a test particle orbiting a Kerr black hole. I am trying to determine what the initial $ \frac{d t}{d\tau} $ would be. On Wikipedia https://en.wikipedia.org/wiki/...
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Symmetries of quasinormal modes of Kerr black hole

I have been reading this following paper on numerical evolution of the Teukolsky equation (see e.g. Eq 1 in their paper) for spin -2 fields about a spinning black hole (Kerr) solution. As the ...
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Gravitational waves from collapsing rotating mass? [closed]

According to the Birkhoff’s theorem, a non-rotating mass does not radiate gravitational waves during a spherically symmetric collapse. There is, however, no equivalent of the Birkhoff’s theorem for a ...
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Why do angular velocity deviates from Keplerian value close to a black hole?

The energy-momentum conservation equation in General Relativity is expressed as $T^{\mu\nu}_{\;\;;\nu}=0$ and by projecting this equation into the space normal to the four-velocity, we obtain the ...
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Does matter take infinite time to leave a black hole?

To this question: Can a sufficiently large black hole be singularity-free? about the possibility of a sufficiently large black hole not containing a singularity John Rennie posted an answer ...
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Some doubts regarding the effective potential for Kerr geometry

In the review Foundations of Black Hole Accretion Disk Theory, the authors defines an effective potential for Kerr geometry as (Chap. 2, eqn. 23) $$\Phi_{eff}=-\frac{1}{2}\ln\left|g^{tt}-2lg^{t\phi}+l^...
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Anatomy of a black hole: which are its layers?

I'm trying to find out how a Kerr-type black hole is structured (that is, a black hole with non-zero angular momentum but no net electrical charge). According to the information I have found, the ...
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What is the volume inside the inner event horizon of a Kerr black hole?

(Dokuchaev 2011) found periodic orbits of particles and photons inside a Kerr-Newman black hole with a maximally extended global geometry. They orbit inside the inner horizon $r<r_-$ where the $r$ ...
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Where is the singularity located in a Kerr black hole?

In a rotating Kerr black hole is the ringlike singularity situated between the inner and the outer event horizon of the black hole?
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The physical interpretation of the trip inside Kerr (black hole) spacetime

Consider then the Kerr metric$[1]$: $$ds^{2} = -\Bigg(1-\frac{2Mr}{\rho^2}\Bigg)dt^2 - \frac{2Marsin^2(\theta)}{\rho^2}[dt d\phi+d\phi dt] +$$ $$+\frac{\rho^2}{\Delta}dr^2+\rho^2d\theta^2+ \frac{sin^...
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Time Derivative defined by Fermi transport in Kerr Space-Time

I have been studying 3+1 GR the last weeks. I have tried to comprehend Electrodynamics in curved space-time: 3+1 formulation (1982) Thorne McDonald I have studied another 3+1 GR book but it didn'...
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Normal vectors and induced metric Kerr metric

Consider the Kerr metric given by: $$ds^2 = -(1-\frac{2GMr}{\rho^2})dt^2 - \frac{2GMar\sin^2{\theta}}{\rho^2}(dtd\phi+d\phi dt)+ \frac{\rho^2}{\Delta}dr^2+\rho^2d\theta^2+ \frac{\sin^2\theta}{\rho^2}[...
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Particle falling into a Kerr black hole

Let's say that a particle starts a radial free fall towards a Kerr black hole with zero initial energy at $r\rightarrow\infty$. The initial angular momentum of the particle is zero ($p_\phi = 0)$. ...
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Teukolsky-Starobinsky identities

The Teukolsky-Starobinsky identites relate solutions of the two Newman-Penrose scalars $\Psi_0$ and $\Psi_4$ around Kerr black holes. For example (here I am quoting Theorem 1 in Sec 81 of ...